Answer:
(a)z=-1
(b)48.5 pounds
(c)61.5 pounds
Step-by-step explanation:
[tex]z-score=\dfrac{x-\mu}{\sigma}[/tex]
Given:
Mean, μ = 55 pounds
Standard deviation,σ = 6 pounds.
(a)For a dog that weighs 49 pounds.
x=49 pounds
The z-score
[tex]=\dfrac{49-55}{6}\\=\dfrac{-6}{6}\\\\=-1[/tex]
(b)When a dog has a z-score of -1.09
[tex]-1.09=\dfrac{x-55}{6}\\x-55=-6.54\\x=55-6.54\\x=48.46 \approx 48.5$ pounds (to the nearest tenth)[/tex]
The weight of a dog with a z-score of -1.09 is 48.5 pounds.
(c)When a dog has a z-score of 1.09
[tex]1.09=\dfrac{x-55}{6}\\x-55=6.54\\x=55+6.54\\x=61.54 \approx 61.5$ pounds (to the nearest tenth)[/tex]
The weight of a dog with a z-score of 1.09 is 61.5 pounds.
If the dog has a z-score of -1.09, his weight is 48.46kg but if the dog has a z-score of 1.09, his weight is 61.54kg
The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean,\sigma=standard\ deviation[/tex]
Given that μ = 55, σ = 6;
For x = 49:
[tex]z=\frac{49-55}{6} =-1[/tex]
If the dog has a z-score of -1.09, his weight is:
[tex]-1.09=\frac{x-55}{6} \\\\x-55=-6.54\\\\x=48.46[/tex]
If the dog has a z-score of 1.09, his weight is:
[tex]1.09=\frac{x-55}{6} \\\\x-55=6.54\\\\x=61.54[/tex]
If the dog has a z-score of -1.09, his weight is 48.46kg but if the dog has a z-score of 1.09, his weight is 61.54kg
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